The optimality system, which is a linear mean-field forward–backward stochastic differential equation with constraint, is obtained by a variational method. By decoupling the optimality system, two coupled Riccati equations and an MF-BSDE are derived. It turns out that the coupled two Riccati equations are uniquely solvable. Then a complete and explicit representation is obtained for the optimal control.
- Linear quadratic optimal control
- Mean-field backward stochastic differential equation
- Optimality system
- Riccati equation
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics